The parallel structure of mathematical reasoning. (English) Zbl 1355.97003

Aberdein, Andrew

Aberdein, Andrew (ed.) et al., The argument of mathematics. Dordrecht: Springer (ISBN 978-94-007-6533-7/hbk; 978-94-007-6534-4/ebook). Logic, Epistemology, and the Unity of Science 30, 361-380 (2013).

From the text: Explaining that success poses a problem for philosophy of mathematics as traditionally conceived. If mathematical practice were ultimately reducible to formal proof, which has been analysed in great detail in mathematical logic, then actual practice would differ only in degree from the elementary and/or foundational work upon which most philosophers of mathematics concentrate. But if mathematical practice cannot be understood solely in such terms, then philosophy of mathematics needs to pay it much closer attention. My goal in this chapter is to address this shortcoming by taking Ruelle’s metaphor seriously, and seeking to devise, as it were, a choreographic notation for the dance which he describes.
For the entire collection see [Zbl 1269.03006].

MSC:

97E50	Reasoning and proving in the mathematics classroom
00A35	Methodology of mathematics
00A30	Philosophy of mathematics

Keywords:

argumentation scheme; mathematical argument; mathematical dialogue; mathematical practice; mathematical proof; mathematical reasoning; Toulmin layout

References:

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